10% of Reggie's savings was $10 more than 40% of Gabriel's savings. After Reggie spent
710 of his savings and Gabriel spent 40% of his savings, Gabriel had $75 less than Reggie. How much was Gabriel's saving at first?
|
Gabriel |
Reggie |
Before |
5 u |
20 u + 100 |
Change |
- 2 u |
- 14 u - 70 |
After |
3 u |
6 u + 30 |
Comparing Gabriel and Reggie in the end |
|
75 more |
10% =
10100 =
110 40% =
40100 =
25 110 Reggie =
25 Gabriel + 10
Make the numerators the same. LCM of 1 and 2 is 2.
1x210x2 Reggie =
2x15x1 Gabriel + 10
220 Reggie =
25 Gabriel + 10
Simplify the fractions.
120 Reggie =
15 Gabriel + 5
Let
15 Gabriel be
1 u.
Gabriel's savings at first = 5 u
120 Reggie =
15 Gabriel + 5
Let
120 Reggie be
1 u + 5.
Reggie's savings at first
= 20 x (1 u + 5)
= 20 u + 100
Savings that Gabriel spent
= 40% x 5 u
=
40100 x 5 u
= 2 u
Savings that Reggie spent
=
710 x (20 u + 100)
= 14 u + 70
Gabriel had $75 less than Reggie in the end. If another $75 was given to Gabriel, the amount that each had in the end would be the same.
6 u + 30 = 3 u + 75
6 u - 3 u = 75 - 30
3 u = 45
1 u = 45 ÷ 3 = 15
Savings that Gabriel had at first
= 5 u
= 5 x 15
= $75
Answer(s): $75